Details

sample199.0ms

Algorithm

intervals

Results

124.0ms	159×	body	1280	valid
26.0ms	52×	body	640	valid
24.0ms	14×	body	2560	valid
7.0ms	19×	body	320	valid
2.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify8.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	10
2	10
1	9
0	6

prune45.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.6b

localize32.0ms

Local error

Found 2 expressions with local error:

0.7b	(- (cos (+ x eps)) (cos x))
2.0b	(cos (+ x eps))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff` `add-cube-cbrt`
4×	`add-log-exp`
3×	`fma-neg`
2×	`expm1-log1p-u` `pow1` `cos-sum` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`associate--l-` `sub-neg` `flip3--` `diff-log` `diff-cos` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 42

Calls

2 calls:

15.0ms	(- (cos (+ x eps)) (cos x))
15.0ms	(cos (+ x eps))

series89.0ms

Counts

2 → 6

Calls

2 calls:

65.0ms	(- (cos (+ x eps)) (cos x))
24.0ms	(cos (+ x eps))

simplify3.1s

Counts

48 → 48

Iterations

Iter	Nodes
done	5000
4	3416
3	1158
2	424
1	202
0	93

prune263.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.5b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
0.3b	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
2.1b	(sin (/ (fma 2 x eps) 2))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
4×	`associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative` `sin-mult`
1×	`associate-*r/` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

38.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
31.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
3.0ms	(sin (/ (fma 2 x eps) 2))

series205.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(* -2 (* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2))))
81.0ms	(* (sin (* eps 1/2)) (sin (/ (fma 2 x eps) 2)))
40.0ms	(sin (/ (fma 2 x eps) 2))

simplify2.7s

Counts

63 → 63

Iterations

Iter	Nodes
done	5001
3	2020
2	602
1	226
0	102

prune434.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.4b

localize19.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (sin (/ eps 2)) -2)
0.3b	(* (* (sin (/ eps 2)) -2) (sin (fma eps 1/2 x)))
2.1b	(sin (fma eps 1/2 x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
6×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`expm1-log1p-u` `sin-sum` `fma-udef` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative`
1×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`

Counts

3 → 55

Calls

3 calls:

9.0ms	(* (sin (/ eps 2)) -2)
39.0ms	(* (* (sin (/ eps 2)) -2) (sin (fma eps 1/2 x)))
2.0ms	(sin (fma eps 1/2 x))

series169.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* (sin (/ eps 2)) -2)
91.0ms	(* (* (sin (/ eps 2)) -2) (sin (fma eps 1/2 x)))
41.0ms	(sin (fma eps 1/2 x))

simplify2.6s

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	2303
2	773
1	252
0	107

prune358.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos x) (sin (/ eps 2)))
0.2b	(* (* (sin x) (sin (/ eps 2))) (cos (/ eps 2)))
0.2b	(* (sin x) (sin (/ eps 2)))
0.3b	(* (* (cos x) (sin (/ eps 2))) (* (sin (/ eps 2)) -2))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`add-sqr-sqrt` `pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`associate-r`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`associate-l`
4×	`expm1-log1p-u` `*-commutative` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`sin-mult` `unswap-sqr`
1×	`associate-*l/`

Counts

4 → 90

Calls

4 calls:

25.0ms	(* (cos x) (sin (/ eps 2)))
45.0ms	(* (* (sin x) (sin (/ eps 2))) (cos (/ eps 2)))
22.0ms	(* (sin x) (sin (/ eps 2)))
48.0ms	(* (* (cos x) (sin (/ eps 2))) (* (sin (/ eps 2)) -2))

series338.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cos x) (sin (/ eps 2)))
105.0ms	(* (* (sin x) (sin (/ eps 2))) (cos (/ eps 2)))
61.0ms	(* (sin x) (sin (/ eps 2)))
96.0ms	(* (* (cos x) (sin (/ eps 2))) (* (sin (/ eps 2)) -2))

simplify1.7s

Counts

102 → 102

Iterations

Iter	Nodes
done	5003
2	1325
1	385
0	160

prune543.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

regimes232.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	19
1	19
0	14

end0.0ms

sample6.5s

Algorithm

intervals

Results

4.1s	4425×	body	1280	valid
987.0ms	618×	body	2560	valid
938.0ms	1901×	body	640	valid
244.0ms	711×	body	320	valid
52.0ms	277×	body	160	valid
7.0ms	68×	body	80	valid